Invariant-Free Clausal Temporal Resolution
Resolution is a well-known proof method for classical logics that is well suited for mechanization. The most fruitful approach in the literature on temporal logic, which was started with the seminal paper of M. Fisher, deals with Propositional Linear-time Temporal Logic (PLTL) and requires generatin...
| Authors: | ; ; ; ; |
|---|---|
| Format: | Article |
| Publication date: | 2011 |
| Country: | España |
| Institution: | Universidad del País Vasco |
| Repository: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/64604 |
| Online Access: | http://hdl.handle.net/10810/64604 |
| Access Level: | Open access |
| Keyword: | propositional linear-time temporal logic resolution invariant-free clausal normal form |
| _version_ | 1878733009361829888 |
|---|---|
| author | Gaintzarain Ibarmia, José |
| author2 | Hermo Huguet, Montserrat Lucio Carrasco, Francisca Navarro, Marisa Orejas, Fernando |
| author2_role | author author author author |
| author_browse | Gaintzarain Ibarmia, José Hermo Huguet, Montserrat Lucio Carrasco, Francisca Navarro, Marisa Orejas, Fernando |
| author_facet | Gaintzarain Ibarmia, José Hermo Huguet, Montserrat Lucio Carrasco, Francisca Navarro, Marisa Orejas, Fernando |
| author_role | author |
| collection | Addi. Archivo Digital para la Docencia y la Investigación |
| description | Resolution is a well-known proof method for classical logics that is well suited for mechanization. The most fruitful approach in the literature on temporal logic, which was started with the seminal paper of M. Fisher, deals with Propositional Linear-time Temporal Logic (PLTL) and requires generating invariants for performing resolution on eventualities. The methods and techniques developed in that approach have also been successfully adapted to obtain a clausal resolution method for Computation Tree Logic (CTL), but invariant handling seems to be a handicap for further extension to more general branching temporal logics. In this paper, we present a new approach to applying resolution to PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Hence, we say that the approach presented in this paper is invariant-free. Our method is based on the dual methods of tableaux and sequents for PLTL that we presented in a previous paper. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called trs-resolution, that extends classical propositional resolution. Finally, we prove that trs-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTL |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_4e482d9eddfa712dce6a8f94652ff24c |
| institution | Universidad del País Vasco |
| instname_str | Universidad del País Vasco |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:addi.ehu.eus:10810/64604 |
| publishDate | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| publisherStr | Springer |
| reponame_str | Addi. Archivo Digital para la Docencia y la Investigación |
| spelling | Invariant-Free Clausal Temporal Resolution Gaintzarain Ibarmia, José Hermo Huguet, Montserrat Lucio Carrasco, Francisca Navarro, Marisa Orejas, Fernando propositional linear-time temporal logic resolution invariant-free clausal normal form Resolution is a well-known proof method for classical logics that is well suited for mechanization. The most fruitful approach in the literature on temporal logic, which was started with the seminal paper of M. Fisher, deals with Propositional Linear-time Temporal Logic (PLTL) and requires generating invariants for performing resolution on eventualities. The methods and techniques developed in that approach have also been successfully adapted to obtain a clausal resolution method for Computation Tree Logic (CTL), but invariant handling seems to be a handicap for further extension to more general branching temporal logics. In this paper, we present a new approach to applying resolution to PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Hence, we say that the approach presented in this paper is invariant-free. Our method is based on the dual methods of tableaux and sequents for PLTL that we presented in a previous paper. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called trs-resolution, that extends classical propositional resolution. Finally, we prove that trs-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTL This work has been partially supported by the Spanish Project TIN2007-66523 and the Basque Project LoRea GIU07/35 Springer http://hdl.handle.net/10810/64604 |
| spellingShingle | Invariant-Free Clausal Temporal Resolution Gaintzarain Ibarmia, José propositional linear-time temporal logic resolution invariant-free clausal normal form |
| title | Invariant-Free Clausal Temporal Resolution |
| title_full | Invariant-Free Clausal Temporal Resolution |
| title_fullStr | Invariant-Free Clausal Temporal Resolution |
| title_full_unstemmed | Invariant-Free Clausal Temporal Resolution |
| title_short | Invariant-Free Clausal Temporal Resolution |
| title_sort | Invariant-Free Clausal Temporal Resolution |
| topic | propositional linear-time temporal logic resolution invariant-free clausal normal form |
| topic_facet | propositional linear-time temporal logic resolution invariant-free clausal normal form |
| url | http://hdl.handle.net/10810/64604 |